1. Field of the Invention
The present invention relates to optical communication, and more specifically, it relates to methods and apparatuses for interleaving frequencies in optical communication systems.
2. Description of Related Art
In dense wavelength division multiplexing (DWDM) optical communication, various frequencies (wavelengths) of laser light are coupled into the same optical fiber. The information capacity is directly proportional to the number of channels in the fiber. Since the total usable wavelength range is limited (about a few tens of nanometers), the smaller the channel spacing, the more channels can fit into the same optical fiber, therefore enabling more communication capacity.
The minimum possible channel spacing is limited by the capability of the multiplexer (MUX) and the de-multiplexer (de-MUX). Currently, the standard channel spacing is 100 GHz (0.8 nm). The manufacturing costs increase dramatically when the channel spacing is less than 100 GHz. A cost-effective method is desirable for interleaving channels thereby enabling the use of higher bandwidth filters with lower channel spacing in an optical communication system. For instance, one can use 100 GHz filters with 50 GHz channel spacing for using a one-stage interleave. Furthermore, if a two-stage interleave is implemented, 100 GHz filters can be used in 25 GHz channel spacing communication system.
FIG. 1A shows a conventional Michelson interferometer. The incident light 10 from the left-hand side of a 50xe2x80x9450 beam-splitter 12 is separated into two beams; 50% of the power is reflected from the beam splitter in beam 14 and the rest of light is transmitted in beam 16. After those two beams are reflected from mirror 18 and mirror 19, they are reflected by and transmitted through the beam-splitter again. The interference takes place at both the bottom and the left of the beam-splitter. The constructive interference takes place when the optical path length difference (OPD) of the two interference beams is an integer multiplication of wavelength. Since the total energy is conserved, the summation of optical power at the bottom arm and the left arm should be equal to the optical power delivered from the light source. In other words, when the constructive interference occurs at the bottom arm, the destructive interference should take place at the left arm and vise verse.
For the interferometer shown in FIG. 1, the amplitudes of the two interference beams are the same and their phase difference depends on the OPD. The various phase functions are listed in Table 1.
Definition of Phase
"psgr"RTM:reflected by BSxe2x86x92reflected by mirrorxe2x86x92transmit through BS.
"psgr"TMRxe2x80x2:transmitted through BSxe2x86x92reflected by mirrorsxe2x86x92reflected by BS.
"psgr"RMR:reflected by BSxe2x86x92reflected by mirrorxe2x86x92reflected by BS
"psgr"TMTxe2x80x2:transmitted by BSxe2x86x92reflected by mirrorxe2x86x92transmit through BS
"psgr"ST:phase introduced by the BS for S-polarized light, transmitted beam with front side incidence
"psgr"STxe2x80x2:phase introduced by the BS for S-polarized light, transmitted beam with rear side incidence
"psgr"SR:phase introduced by the BS for S-polarized light, reflected beam with front side incidence
"psgr"SRxe2x80x2:phase introduced by the BS for S-polarized light, reflected beam with rear side incidence
"psgr"PT:phase introduced by the BS for P-polarized light, transmitted beam with front side incidence
"psgr"PTxe2x80x3:phase introduced by the BS for P-polarized light, transmitted beam with rear side incidence
"psgr"PR:phase introduced by the BS for P-polarized light, refleced beam with front side incidence
"psgr"PRxe2x80x2:phase introduced by the BS for P-polarized light, reflected beam with rear side incidence
"psgr"B="psgr"TRMxe2x80x2xe2x88x92"psgr"RMT(phase difference of the two interference beams in the bottom arm)
"psgr"L="psgr"TMTxe2x80x2xe2x88x92"psgr"RMR(phase difference of the two interfereince beams in the left arm)
Power Definition
PB:optical power in the bottom arm
PL: optical power in the left arm
Assuming that the incident polarization is S-polarized, the two electric fields at the bottom arm can be expressed as follows.                     E        →                    TMR        xe2x80x2              =                            s          ^                2            ⁢              xe2x80x83            ⁢              exp        ⁡                  (                      ⅈ            ⁢                          xe2x80x83                        ⁢                          Ψ                              TMR                xe2x80x2                                              )                                        E        →            RMT        =                            s          ^                2            ⁢              xe2x80x83            ⁢              exp        ⁡                  (                      ⅈ            ⁢                          xe2x80x83                        ⁢                          Ψ              RMT                                )                    
The power at the bottom arm is as follows.                                                         P              B                        =                                                            "LeftDoubleBracketingBar"                                                                                    E                        →                                                                    TMR                        xe2x80x2                                                              +                                                                  E                        →                                            RMT                                                        "RightDoubleBracketingBar"                                2                            =                                                                    "LeftDoubleBracketingBar"                                                                  s                        ^                                            ⁢                                              xe2x80x83                                            ⁢                                              cos                        ⁡                                                  [                                                                                                                    ψ                                                                  TMR                                  xe2x80x2                                                                                            -                                                              ψ                                RMT                                                                                      2                                                    ]                                                                                      "RightDoubleBracketingBar"                                    2                                =                                                      cos                    2                                    ⁡                                      (                                          ψ                      2                                        )                                                                                ⁢                      
                    ⁢          With                ⁢                  xe2x80x83                                    Equation        ⁢                  xe2x80x83                ⁢                  (          1          )                                                              ψ                          TMR              xe2x80x2                                =                                    2              ⁢                              xe2x80x83                            ⁢                              π                ⁡                                  (                                      v                                          v                      1                                                        )                                                      +                          ψ              ST                        +                          ψ                              SR                xe2x80x2                                                    ⁢                  
                ⁢                              ψ            RMT                    =                                    2              ⁢                              xe2x80x83                            ⁢                              π                ⁡                                  (                                      v                                          v                      2                                                        )                                                      +                          ψ              SR                        +                          ψ              ST                                      ⁢                  
                ⁢                              ψ            B                    =                                                    ψ                B                                  (                  s                  )                                            ≡                                                ψ                                      TMR                    xe2x80x2                                                  -                                  ψ                  RMT                                                      =                                          2                ⁢                                  xe2x80x83                                ⁢                                  π                  ⁡                                      (                                          v                                              v                        0                                                              )                                                              +                              (                                                      ψ                                          SR                      xe2x80x2                                                        -                                      ψ                    SR                                                  )                                                    ⁢                  
                ⁢        where        ⁢                  xe2x80x83                ⁢                  "IndentingNewLine"                ⁢                                            v              1                        =                          C                              2                ⁢                                  L                  1                                                              ;                      xe2x80x83                    ⁢                                    v              2                        =                          C                              2                ⁢                                  L                  2                                                              ;                      xe2x80x83                    ⁢                                    v              0                        =                          C                              2                ⁢                                  (                                                            L                      1                                        -                                          L                      2                                                        )                                                                                        Equation        ⁢                  xe2x80x83                ⁢                  (          2.1          )                    
In Equation (1), the total power on the bottom arm is dependant on the phase difference between the two interference beams.
When the incident polarization is P-polarized,                               ψ          B                =                                            ψ              B                              (                p                )                                      ≡                                          ψ                                  TMR                  xe2x80x2                                            -                              ψ                RMT                                              =                                    2              ⁢                              xe2x80x83                            ⁢                              π                ⁡                                  (                                      v                                          v                      0                                                        )                                                      +                          (                                                ψ                                      PR                    xe2x80x2                                                  -                                  ψ                  PR                                            )                                                          Equation        ⁢                  xe2x80x83                ⁢                  (          2.2          )                    
The phase difference of the two interference beams at the bottom arm for S-polarized light, "psgr"(s)B, and that of P-polarized light, "psgr"(p)B, will be the same when xcexa8SRxe2x88x92xcexa8SRxe2x80x2=xcexa8PRxe2x88x92xcexa8PRxe2x80x2. In the following analysis at this section, it is assumed that the coating of beam splitter has been made such that xcexa8SRxe2x88x92xcexa8SRxe2x80x2=xcexa8PRxe2x88x92xcexa8PRxe2x80x2=0. Under such condition, "psgr"B="psgr"(s)B="psgr"(p)B. Notice that in the derivation of equations (2.1) and (2.2), the phase introduced from the two reflection mirrors is neglected. Those phases do not have polarization dependence due to the fact that the incident angles at those surfaces are close to normal.
FIG. 2 shows the phase difference "psgr"B and "psgr"L. Both of them are a linear function of frequency with slope 2 Πvxe2x88x921o. As a result of energy conservation, there is a phase offset xcfx80 between them. FIG. 3 shows the corresponding optical power at the bottom (upper curve at 0 normalized frequency) and left arm (bottom curve at 0 normalized frequency). In these plots, the horizontal axis is normalized by frequency vo. When the normalized frequency is an integer, all the light goes to the bottom; In contrast, as that is a half integer, the light goes to the left In other world, the light is interleaved in the frequency domain with half of the channels (integer frequency) to the bottom arm and the other half to the left arm.
The Michelson interferometer shows the fundamental requirement of interleaving. However, it is not practical to apply such an interferometer to a real interleave device since it is too sensitive to the central frequency and the line width of light source. Referring to FIG. 3, as the frequency is slightly off from the integer, part of the optical power will leak from the bottom arm towards the left arm, causing cross talk between channels. In other words, in order to make this device work, the laser line width should be zero and its central frequencies have to be perfectly locked over all the operation condition. Such frequency locking is very hard to achieve in the real world.
It is an object of the present invention to provide an optical filtering method to separate/merge the odd and even channels in an optical communication system.
It is another object of the invention is to provide and optical interleaver that utilizes an interferometer where one beam carries a linear phase and the other beam carries a non-linear phase such that the frequency dependence of the phase difference, "psgr"B, between these two arms has a step-like function
Still another object of the invention is to provide an optical interleaver that enables the use of higher bandwidth filters to have lower channel spacing communication system.
Another object of the invention is to provide optical interleaver methods and apparatuses that cost much less than existing interleaver devices and perform better.
These and other objects of the invention will be apparent to those skilled in the art based on the teachings herein.
This invention is an interleave device using an optical interferometer where one of the beams carries a linear phase and the other beam carries a non-linear phase such that the frequency dependence of the phase difference between these two arms has a step-like function. The present invention uses a non-linear phase generator (NLPG) to make the phase a non-linear function of optical frequency.
In one embodiment, a non-linear phase generator is a mirror made by a cavity. A first surface of the cavity has reflectivity less than one and the second reflection surface has reflectivity near 100%. As the light is incident onto the NLPG, it undergoes multiple reflections. When the static state is achieved, the amplitude of reflected light should be near 100% since the second reflecting surface reflects all of the incident optical power. The phase of the reflected light depends on the frequency of light and the physical properties of the cavity. For non-zero reflectivity of the first surface, the multiple reflections cause the phase to be a non-linear function of frequency.
In one embodiment of the invention, a modified Michelson interferometer, replaces a mirror with a cavity. The phase of the light beam reflecting from the cavity is a non-linear function of optical frequency. The phase of the other beam is a linear function of optical frequency. The dependence of the phase difference of these two beams on optical frequency is a step-like function with step Π.
The polarization dependent feature of phase of each beam can result in certain problems. When the phase difference has polarization dependence, the interference fringe will peak at different frequencies. Therefore, when the incident polarization includes both P and S, the fringe contrast will be degraded. Secondly, when the transmission curve is perfect for the S-polarized light, the phase offset in the P-polarized light worsens the performance of the channel isolation. The present invention provides several techniques for compensating for the polarization dependent feature of phase of each beam. This disclosure provides examples of a variety of embodiments of step-phase interferometers usable in the present invention.